1) the sum of the digits of a two digit number is 9. The value of the number is 12 times the tens digit. Find the number.
2) the sum of the digits of a two digit number is 12. If 15 is added to the number the result is 6times the units digit. Find the number.
Please help!!
Thanks (:
let the unit digit by x
let the tens digit be y
so x+y=9, both x and y being whole numbers
value of number = 10y+x
given: 10y+x = 12y
or x = 2y
back in the first:
x+y=9
2y+y=9
y=3, and thus x = 6
the number is 36
let's see you do the second question in the same way.
Thanks ! This really helped (:
Certainly! Let's solve these problems step by step.
Problem 1:
We need to find a two-digit number where the sum of its digits is 9, and the value of the number is 12 times the tens digit.
Let's assume the tens digit is 'x,' and the units digit is 'y.'
According to the statement, the sum of the digits is 9:
x + y = 9 ----> (Equation 1)
The value of the number is 12 times the tens digit:
10x + y = 12x ----> (Equation 2)
To solve this system of equations, we can use substitution or elimination method.
Let's solve it using substitution method:
From Equation 1, we can express y in terms of x:
y = 9 - x
Substituting it in Equation 2:
10x + (9 - x) = 12x
9 = 3x
x = 3
Now, substitute the value of x back into Equation 1 to find y:
3 + y = 9
y = 6
Therefore, the number is 36.
Problem 2:
We need to find a two-digit number where the sum of its digits is 12, and if 15 is added to the number, the result is 6 times the units digit.
Let's assume the tens digit is 'a,' and the units digit is 'b.'
According to the statement, the sum of the digits is 12:
a + b = 12 ----> (Equation 1)
If 15 is added to the number, it is equal to 6 times the units digit:
10a + b + 15 = 6b ----> (Equation 2)
Again, we'll solve this system of equations using substitution method.
From Equation 1, we can express b in terms of a:
b = 12 - a
Substituting it in Equation 2:
10a + (12 - a) + 15 = 6(12 - a)
10a + 12 - a + 15 = 72 - 6a
9a + 27 = 72 - 6a
15a + 27 = 72
15a = 45
a = 3
Now, substitute the value of a back into Equation 1 to find b:
3 + b = 12
b = 9
Therefore, the number is 39.
Hope this helps! If you have any more questions, feel free to ask.